Small carbon clusters (C-n, n = 2-15) are produced in a molecular beam by pulsed laser vaporization and studied with vacuum ultraviolet (VUV) photoionization mass spectrometry. The required VUV radiation in the 8-12 eV range is provided by the Advanced Light Source (ALS) at the Lawrence Berkeley National Laboratory. Mass spectra at various ionization energies reveal the qualitative relative abundances of the neutral carbon clusters produced. By far the most abundant species is C-3. Using the tunability of the ALS, ionization threshold spectra are recorded for the clusters up to 15 atoms in size. The ionization thresholds are compared to those measured previously with charge-transfer bracketing methods. To interpret the ionization thresholds for different cluster sizes, new ab initio calculations are carried out on the clusters for n = 4-10. Geometric structures are optimized at the CCSD(T) level with cc-pVTZ (or cc-pVDZ) basis sets, and focal point extrapolations are applied to both neutral and cation species to determine adiabatic and vertical ionization potentials. The comparison of computed and measured ionization potentials makes it possible to investigate the isomeric structures of the neutral clusters produced in this experiment. The measurements are inconclusive for the n = 4-6 species because of unquenched excited electronic states. However, the data provide evidence for the prominence of linear structures for the n = 7, 9, 11, 13 species and the presence of cyclic C-10.